- 标题
- 摘要
- 关键词
- 实验方案
- 产品
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[IEEE 2018 26th European Signal Processing Conference (EUSIPCO) - Rome (2018.9.3-2018.9.7)] 2018 26th European Signal Processing Conference (EUSIPCO) - Uncertainty Quantification in Imaging: When Convex Optimization Meets Bayesian Analysis
摘要： We propose to perform Bayesian uncertainty quantification via convex optimization tools (BUQO), in the context of high dimensional inverse problems. We quantify the uncertainty associated with particular structures appearing in the maximum a posteriori estimate, obtained from a log-concave Bayesian model. A hypothesis test is defined, where the null hypothesis represents the non-existence of the structure of interest in the true image. To determine if this null hypothesis is rejected, we use the data and prior knowledge. Computing such test in the context of imaging problem is often intractable due to the high dimensionality involved. In this work, we propose to leverage probability concentration phenomena and the underlying convex geometry to formulate the Bayesian hypothesis test as a convex minimization problem. This problem is subsequently solved using a proximal primal-dual algorithm. The proposed method is applied to astronomical radio-interferometric imaging.
关键词： astronomical imaging,proximal primal-dual algorithm,inverse problem,hypothesis testing,Bayesian uncertainty quantification
更新于2025-09-23 15:23:52
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Terahertz Differential Computed Tomography: a Relevant Nondestructive Inspection Application
摘要： In recent years, tremendous advances have been made in the choice of materials used in the industry. With weight reduction as the goal, composite and polymer materials are more and more popular but they are almost transparent to X-ray. Because of this, interest has grown in other wavelengths like terahertz (THz). Due to a difference in how X-ray and THz propagate, X-ray CT algorithms cannot be directly used. For example, THz induces refraction making the reconstruction problem nonlinear. In this paper, we present a new algorithm which complies with beam profile intensities, refraction, and reflection. It is based on linearizing the reconstruction process around a computer-aided design (CAD) model of the object to be reconstructed. The method we propose computes the deviation between the object and this model.
关键词： Terahertz computed tomography,Inverse problem,Nondestructive testing,Modeling,Monte Carlo,Refraction,Nonlinear problem,Projection simulation
更新于2025-09-23 15:22:29
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A Coefficient Inverse Problem with a Single Measurement of Phaseless Scattering Data
摘要： We present a reconstruction method for solving a 3D coefficient inverse problem with a single measurement of phaseless scattering data. These are multifrequency data generated by a single direction of the incident plane wave. Our method consists of two stages, each of which is challenging in its own right. The first stage is the problem of the reconstruction of the wave field itself on the measurement plane from the measured intensity. In this stage, we prove a uniqueness result and study a numerical method for this reconstruction. After obtaining the approximate scattered field on the measurement plane, in the second stage, we exploit our newly developed globally convergent numerical method to solve the coefficient inverse problem with the phased scattering data. Our two-stage method does not require any advanced information about the true solution of the phaseless coefficient inverse problem. Numerical examples are presented to demonstrate the performance of the method.
关键词： phaseless inverse scattering,reconstruction method,one measurement,uniqueness theorems,coefficient inverse problem
更新于2025-09-23 15:22:29
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Variational source condition for ill-posed backward nonlinear Maxwell's equations
摘要： This paper examines the mathematical analysis of an electromagnetic inverse problem governed by nonlinear evolutionary Maxwell’s equations. The aim of the inverse problem is to recover electromagnetic ?elds at the past time by noisy measurement data at the present time. We consider the Tikhonov regularization method to cope with the ill-posedness of the governing backward nonlinear Maxwell’s equations. By means of the semigroup theory, we study its convergence analysis and derive optimality conditions through a rigorous ?rst-order analysis and adjoint calculus. The ?nal part of the paper is focused on the convergence rate analysis of the Tikhonov regularization method under a variational source condition (VSC), which leads to power-type convergence rates. Employing the spectral theory, the complex interpolation theory and fractional Sobolev spaces, we validate the proposed VSC on account of an appropriate regularity assumption on the exact initial data and the material parameters.
关键词： convergence rate analysis,electromagnetic inverse problem,variational source condition,nonlinear Maxwell’s equations,Tikhonov regularization
更新于2025-09-23 15:21:21
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[IEEE 2018 IEEE International Conference on Computational Electromagnetics (ICCEM) - Chengdu (2018.3.26-2018.3.28)] 2018 IEEE International Conference on Computational Electromagnetics (ICCEM) - Complex-Valued Deep Convolutional Networks for Nonlinear Electromagnetic Inverse Scattering
摘要： Electromagnetic inverse scattering problem is a typical complex problem while traditional deep convolutional neural network can only be applied to real problem. Motivated by this, this paper presents a new approach for electromagnetic inverse problem with complex convolutional neural network. In this way, several cascaded convolutional neural network modules are introduced to learn a model to realize super-resolution for electromagnetic imaging. The simulation and experimental results show that the proposed method paves a new way addressing real-time practical large-scale electromagnetic inverse scattering problems.
关键词： super-resolution,electromagnetic imaging,convolutional neural network,electromagnetic inverse problem
更新于2025-09-23 15:21:21
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[IEEE 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring) - Rome, Italy (2019.6.17-2019.6.20)] 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring) - Stability of Least Squares for the Solution of an Ill-posed Inverse Problem of Reconstructing Real Value of the Pcrrnittivity of a Dielectric Layer in a Rectangular Waveguide
摘要： We use the solution to Maxwell’s equations in a rectangular single-mode waveguide with multi-mode boundary conditions at its flanges to determine the parameters of the inclusion. The well-posedness of the inverse problem is studied using explicit expressions for the S-parameters of the waveguide when the inclusion is a plane-parallel dielectric slab. The methods of reconstructing permittivity from the measured (experimental) data must be stable and well-conditioned. The importance of these demands is discussed taking as an example the determination of real permittivity from noisy measurement data of the transmission coefficient of the principal waveguide mode. Generally, this problem is unsolvable because the range of the function to be inverted forms a set of measure zero on the complex plane. In addition, the occurrence of self-intersections of the parametric curve leads to non-uniqueness of the solution to the inverse problem. Therefore, approximate methods of the permittivity reconstruction in the vicinity of such points may be unstable or ill-conditioned. In our study, we present several examples of such algorithms. We demonstrate that the method of least squares applied for reconstructing permittivity of the inclusion from multi-frequency measurement data is a stable algorithm for the solution to this inverse problem. This approach does not use a priori estimates for the sought parameter and information about the location of singularities of the parametric curve. We determine the interval of variation of the condition number for the method of least squares and show that this quantity decreases as one of the following parameters increases: the width of the dielectric layer, the measurement frequency band, or its distance to the lower cutoff value. Using these results, we estimate the rate of convergence of the approximate solution to the exact value of the sought parameter when the quality of the measurement data is improved and show how to choose optimal parameters of the experiment and the measurement setup.
关键词： inverse problem,permittivity,Maxwell’s equations,waveguide,least squares method
更新于2025-09-23 15:21:01
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On Estimating the Laws of Radial Inhomogeneity in a Cylindrical Waveguide
摘要： The inverse problem about reconstruction of a function characterizing the variation of the elastic modulus in an inhomogeneous cylindrical waveguide according to information about the field of radial displacements in the far zone has been studied. A study has been carried out based on combining the Fourier transform and linearization method. Each step of the formed iteration process includes the solution of the direct problem based on the shooting method and the solution of a Fredholm integral equation of the first kind for finding the refining corrections for the sought function. The results of computational experiments are presented.
关键词： field in the far zone,cylindrical waveguide,variable Young modulus,inverse problem
更新于2025-09-23 15:19:57
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[Communications in Computer and Information Science] Supercomputing Volume 965 (4th Russian Supercomputing Days, RuSCDays 2018, Moscow, Russia, September 24–25, 2018, Revised Selected Papers) || Numerical Method for Solving a Diffraction Problem of Electromagnetic Wave on a System of Bodies and Screens
摘要： The three-dimensional vector problem of electromagnetic wave di?raction by systems of intersecting dielectric bodies and in?nitely thin perfectly conducting screens of irregular shapes is considered. The original boundary value problem for Maxwell‘s equations is reduced to a system of integro-di?erential equations. Methods of surface and volume integral equations are used. The system of linear algebraic equations is obtained using the Galerkin method with compactly supported basis functions. The subhierarchical method is applied to solve the di?raction problem by scatterers of irregular shapes. Several results are presented. Also we used a parallel algorithm.
关键词： Inverse problem of di?raction,Integro-di?erential equation,Permittivity tensor,Tensor Green’s function,Boundary value problem
更新于2025-09-19 17:15:36
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Bayesian 3D X-Ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain
摘要： In this paper, a hierarchical prior model based on the Haar transformation and an appropriate Bayesian computational method for X-ray CT reconstruction are presented. Given the piece-wise continuous property of the object, a multilevel Haar transformation is used to associate a sparse representation for the object. The sparse structure is enforced via a generalized Student-t distribution (S tg), expressed as the marginal of a normal-inverse Gamma distribution. The proposed model and corresponding algorithm are designed to adapt to specific 3D data sizes and to be used in both medical and industrial Non-Destructive Testing (NDT) applications. In the proposed Bayesian method, a hierarchical structured prior model is proposed, and the parameters are iteratively estimated. The initialization of the iterative algorithm uses the parameters of the prior distributions. A novel strategy for the initialization is presented and proven experimentally. We compare the proposed method with two state-of-the-art approaches, showing that our method has better reconstruction performance when fewer projections are considered and when projections are acquired from limited angles.
关键词： Haar transformation,X-ray computed tomography,generalized Student-t distribution,hierarchical structure,inverse problem,sparsity
更新于2025-09-19 17:15:36
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PDE-based numerical method for a limited angle X-ray tomography
摘要： A new numerical method for X-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This method is based on the analysis of the transport PDE governing the X-ray tomography rather than on the conventional integral formulation. The quasi-reversibility method is applied. Convergence analysis is performed using a new Carleman estimate. Numerical results are presented and compared with the inversion of the Radon transform using the well-known filtered back projection algorithm. In addition, it is shown how to use our method to study the inversion of the attenuated X-ray transform for the same case of incomplete data.
关键词： X-ray transform,Carleman estimate,incomplete data,tomographic inverse problem
更新于2025-09-19 17:15:36